Anis Matoussi

Professor, Applied Mathematics at Le Mans University
Director of Risk and Insurance Institute of Le Mans
Head of Master Actuarial Science
Research Associate at CMAP-Ecole Polytechnique                                                                           


 Le Mans University 
 Risk and Insurance Institute of Le Mans 
LMM & FR CNRS N°2962 
 Avenue Olivier Messiaen 

 F-72085 Le Mans Cedex 9, France 
 Téléphone : + 33(0)2 43 83 37 19 
 Courrier électronique : anis.matoussi@

 - ANR CAESARS 2016-2019 (Control and simulAtion of Electrical Systems, interAction and RobustnesS), see website.
-  Spring School CREMMA, see website

Research Interest

  • Backward Stochastic Differential Equations (BSDEs) :
    • Second order BSDEs
    • Reflected BSDEs with one and two barriers
    • Obstacle problem for Nonlinear PDE
  • Stochastic control applied to mathematical finance,  insurance and energy
    • Stochastic control under uncertainty
    • Optimal allocation and investment
    • Control and simulation of electrical systems
  • Stochastic nonlinear  PDEs
    • Maximum principle and obstacle problem for quasilinear SPDEs.
    • Numerical computation and Monte Carlo methods
    • Probabilistic representation for fully nonlinear SPDEs (classical and viscosity solution)

Recent Papers

41. L. Denis,  A. Matoussi, C. Zhou. Second order BSDEs with jumps by measurable selection argumentsPreprint (2018).

40. L. Denis,  A. Matoussi, F. Noubiagain. Generalized Reflected second order BSDEsPreprint (2018).

39. N. El Karoui, A. Matoussi, A. Ngoupeyou. Quadratic Exponential  semimartingales and Applications to  BSDE with jumps. arXiv:1603.06191 (2016).

38. M. Jeanblanc, A. Matoussi, A. Ngoupeyou. Robust utility maximization in a discontinuous filtration.  arXiv:1201.2690v2 (last version 2016), submitted

Accepted Papers

37.  A. Matoussi, W. Sabbagh, T. Zhang. Large Deviation of Obstacle Problems for Quasi-linear Stochastic PDEs arXiv:1712.02169 (2017),   to appear in Applied Mathematics and Optimization (2019),
36. C. Alasseur, IBen Taher,  A. Matoussi. An Extended Mean Field Game For Storage in Smart GridsarXiv:1710.08991v2 (2018),  to appear in Journal of Optimization Theory and Applications (2019).
35. A. Bachouch, A. Matoussi.  L2 -Regularity for the solutions of Forward Backward Doubly Stochastic Differential Equations under globally Lipschitz continuous coefficients. hal-01548712 (2017), in revision (minor)  at  Stochastics and Dynamics (2019).
34. A. Matoussi,  D. Possamai  and C.  Zhou. Corrigendum for "Second order reflected backward stochastic differential equations" and "Second-order BSDEs with general reflection and Dynkin games under uncertainty".  arXiv:1706.08588 (2017), in revision (minor) at Annals of Applied Probability (2019).
33. A. Matoussi, D. Possamai, W. Sabbagh. Probabilistic Interpretation for Viscosity Solution of Fully Nonlinear SPDE's.  Probability Theory and Related Fields, 174 (1), 177-233 (2019).
32. A. Matoussi, H. Xing. Convex Duality for stochastic  Differential Utility. Mathematical Finance, 28 (4), 989-1019 (2018).
31. W. Faidi, A. Matoussi, M. Mnif. Robust utility maximization with a general penality term.  arXiv :1302.0442.  International Journal of Theoretical and Applied Finance, Vol. 20, N°. 3, 750015 (2017). 
30A. Matoussi, W. Sabbagh, T. Zhang. Backward doubly SDEs and semilinear SPDEs in a convex domain. Stochastic Processes and Their Applications Vol. 127,  N°. 9, 2781–2815  (2017). 
29. A. Matoussi, L. Piozin, A. Popier.  Stochastic PDEs with singular terminal condiontion.  Stochastic Processes and Their Applications, Vol. 127,  N°. 3, 831–876  (2017). 
28. A. Matoussi, W. Sabbagh. Numerical computation for backward doubly SDEs with random terminal time. Monte Carlo Methods Appl. 22, no. 3, 229–258 (2016).
27. A. Bachouch., E. Gobet, A. Matoussi.  Emperical Regression Method for Backward doubly SDEs, SIAM/ASA Journal on Uncertainty Quantification (JUQ), Vol. 4,  N°. 1, 358–379 (2016). 
26. A. Bachouch, M.-A. Ben Lasmar, A. Matoussi, M. Mnif. Euler time discretization of Backward Doubly SDEs and Applications to Semilinear SPDEs, Stochastic Partial Differential Equations : Analysis and Computations, 1, 1–43 (2016).                                    
25. Y. Hu, A. Matoussi, T. Zhang. Wong-Zakai approximation for Backward doubly SDEs. Stochastic  Processes and Their Applications, Vol. 125 (12), 4375-4404 (2015).       
24. A. Matoussi, H. Mezghani, M. Mnif. Maximization of recursive utilities under convex portfolio constraints.  Applied Mathematics and Optimization. Vol. 71 (2), 313-351 (2015). 
23A. Matoussi, D. Possamai and C. Zhou. Robust Utility Maximization in Non-dominated Models with 2BSDE : the Uncertain Volatility Model. Mathematical FinanceVol. 25, N°. 2, 258-287 (2015). 
22. L. Denis, A. Matoussi, J. Zhang. The Obstacle Problem for quasilinear SPDEs with non- homogeneous operator.  Discrete and Continuous Dynamical Systems Series A"(DCDS-A), Vol. 35,  N°. 11,  5185-5202 (2015). 
21. L. Denis, A. Matoussi, J. Zhang. The existence and uniqueness result for Quasilinear Stochastic PDEs with Obstacle under weaker integrability conditions. Stochastics and Dynamics, Vol. 15, N°.4, 1550023  (2015).
20A. Matoussi, W. Sabbagh, C. Zhou. The obstacle problem for semilinear parabolic partial integro-differential equations.  Stochastics and Dynamics Vol. 15, N°.1, 1550007 (2015).  
19.  L. Denis, A. Matoussi, J. Zhang. Maximum principle for quasilinear SPDEs with obstacle. Electronic  Journal of ProbabilityVol. 19, Issue 44, 1-32 (2014). 
18. A. Matoussi, L. Piozin, D. Possamai. Second-order BSDEs with general reflection and Dynkin games under uncertainty. Stochastic Processes and Their Applications, Vol. 124, Issue 7, 2281–2321 (2014).
17. L. Denis, A. Matoussi and J. Zhang. The Obstacle problem for quasilinear SPDEs : Analytical approach. The Annals of Probabilty, Vol. 42, No.3, 865–905 (2014). 
16. A. Matoussi,  D. Possamai  and C.  Zhou. Second order reflected backward stochastic differential equations. Annals of Applied Probability, Vol. 23, No. 6, 2420–2457, (2013).
15. L. Denis, A. Matoussi. Maximum principle for quasilinear SPDE’s on a bounded domain without regularity assumptions. Stochastic Processes and Their Applications 123, 1104–1137 (2013).
14. W. Faidi, A. Matoussi, M. Mnif.  Maximization of Recursive Utilities: A Dynamic Maximum Principle Approach.  SIAM J. of Financial Math., Vol. 2, pp. 1014-1041 (2011). 
13. A. Matoussi,  L. Stoica. The Obstacle Problem for Quasilinear Stochastic PDE's. Annals of Probability, Vol. 38, N.3, 1143-1179 (2010).
12. L. Denis, A. Matoussi, L. Stoica. Moser iteration applied to parabolic SPDE’s: first approach. Quaderni di Matematica, Series edited by Dipartimento di Matematica     
Seconda Università di Napoli. Proceeding "Stochastic Partial Differential Equations and Applications – VIII" (Levico, Jan. 6-12, 2008), (2010). 
11. L. Denis,  A. Matoussi, L. Stoica. Maximum principle and comparison theorems for solutions of Quasilinear SPDE's. Electronic Journal of Probability 14, pp. 500-530 (2009).
10. S. Crépey, A. Matoussi. Reflected and Doubly Reflected BSDEs with jumpsAnnals of  Applied Probability 18, No. 5, pp. 2041-2069 (2008).
 9. A. Matoussi, M. Xu. Sobolev solution for semilinear PDE with obstacle under monotonocity condition. Electronic Journal of Probability  Vol. 13, No.35, 1035-1067 (2008).
 8. G. Bordigoni, A. Matoussi, M. Schweizer. A stochastic control approach to a robust utility maximization problem. Abel Symposium 2005. Stochastic Analysis and Applications, eds. F.E. Benth, G. Di Nunno, T. Lindstrom, B. Oksendal, T. Zhang. Springer-Verlag Berlin, pp. 125-151 (2007).
 7. L. Denis,  A. Matoussi, L. Stoica. Lp-estimates for the uniform norm of solutions quasilinear SPDE's.  Probability Theory and Related Fields, 133, pp. 437-463 (2005).
 6. J.-P. Lepeltier, A. Matoussi, M. Xu. Reflected BSDE with monotonicity condition and general increasing growth conditionAdvances in Applied Probability 37, 134-159 (2005).
 5. S. Dereich, F. Fehringer, A. Matoussi and M. Scheutzow : On the link between small ball probabilities and the quantization problem for Gaussian measures on Banach spaces.  Journal of Theoretical Probability 16, 249-265 (2003).
 4. A. Matoussi, M. Scheutzow. Semilinear Stochastic PDE's with nonlinear noise and Backward Doubly SDE's.  Journal of Theoretical Probability 15, 1-39 (2002).
 3. V. Bally, A. Matoussi. Weak solutions of Stochastic PDEs and Backward doubly stochastic differential equationsJournal of Theoretical Probability 14, 125-164 (2001). 
 2. S. Hamadène, J.P. Lepeltier, A. Matoussi.  Double Barrier Reflected BSDEs with continuous coefficient. Backward stochastic differential equations. N. El Karoui and 
 L. Mazliak (Editors). Pitman Research Notes in Mathematics Series (1997).
 1. A. Matoussi. Reflected solutions of BSDEs with continuous coefficientStatistics and Probability Letters 34, 347-354 (1997).

Chapter in Books

N. EL Karoui, S. Hamadène, A. Matoussi.  Backward stochastic differential equations and applications. Chapter 8 in the book "Indifference Pricing: Theory and Applications" edited by René Carmona, Springer-Verlag  pp. 267-320 (2008).

Current PhD Students

- Chefia  ZIRI (2018-), co-supervisor Mohamed Mnif,  ENIT-LAMSIN, University Tunis El Manar, Tunisia.

- Arij MANAI (2015-), co-supervisor Habib Ouerdiane, Faculty of Sciences, University Tunis El Manar, Tunisia.

- Rym SALHI  (2015-), co-supervisor Habib Ouerdiane, Faculty of SciencesUniversity Tunis El Manar, Tunisia.

Former PhD Students

Fanny Larissa NOUBIAGAIN Chomchie (2013-2017),  currently Manager of MIRA project at Recherche Departement of ALTRAN, Paris.

- Lambert PIOZIN (2011- 2015), currently junior Quant at HSBC London (UK).

- Anis BEN LASMAR (2010-2015),  currently Assistant Professor at ESPRIT (Engineers School), Tunis (Tunisia).

- Hanen MEZGHANI (2011-2015), currently Assistant Professor  at University of Gafsa (Tunisia).

- Wissal SABBAGH (2011-2014),  currently  Postdoc at University of Evry (France).

- Achref BACHOUCH (2010-2014), currently Postdoc at Humboldt University of Berlin (Germany).

- Jing ZHANG (2009-2012),  currently Assistant Professor  at Fudan University (Shanghai, Chine).  

- Wahid FAIDI (2008-2012),  currently Assistant Professor  at University of Tunis  El Manar (Tunisia).

- Chao ZHOU (2009-2012),  currently Assistant Professor  at National University of Singapore.

- Armand NGOUPEYOU (2007-2010),  currently  Risk manager at Central Bank of Africa (Cameroune).

- Hao WANG (2006-2009),  currently  Risk manager at Bank of China (Jinan, China)